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On conditions implying that continuous linear functionals does not exist. Pt 1

100%

Jama D. , Kaczmarek K. , Wituła R. , Hetmaniok E.

Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska

2011

tom z. 1

29--35

In this paper we discuss some problems concerning the existence of continuous linear functionals in the real L²([0, 1]) space.

Niniejszy artykuł poświęcony jest omówieniu pewnych zagadnień dotyczących istnienia funkcjonałów liniowych ciągłych w rzeczywistej przestrzeni L²([0, 1]).

First principles studies of SnO at different structures

100%

Erdem I. , Hüseyin Kart H. , Cagin T.

2010

tom Vol. 45, nr 2

108-113

Purpose: Structural and mechanical properties of the Sn (tin) based oxides SnO and SnO2 are investigated. The aim of this study to determine in which structural phase SnO is found and to calculate its elastic constants at different pressures. Design/methodology/approach: Calculations have been made for three different structures of SnO by density functional theory (DFT). The behavior of structural parameters (lattice constants, internal parameters) and bulk modulus under different pressures, and elastic constants are calculated by using ab initio calculations. Generalized Gradient Approximation (GGA) and Perdew-Burke-Ernzerhof (PBE) parameterization is used. Findings: All of six elastic constants of litharge SnO and three elastic constants of rocksalt structure of SnO are calculated for the first time in this study. Among three structures of SnO, namely, rocksalt, cesium chloride and tetragonal litharge, the most energetically favorable one is the litharge structure at ambient conditions. The calculation of enthalpies with respect to pressure shows that any phase transition from litharge to rocksalt structure does not occur by applying the pressures of up to 5 GPa to the systems. Equilibrium volume, energy and bulk modulus of rutile SnO2 are also calculated. Our results are compared with other available experimental data and theoretical results. Research limitations/implications: Computer calculation speeds and its information storage area are limitations, it will be possible to reach experimental results as near as in condition that they are improved. Practical implications: It is very difficult to measure elastic constants especially under high pressure experimentally. However, they are calculated by first principles calculations. Originality/value: Behavior of elastic constants and structural parameters under high pressures are determined for the first time in this study. Simulations can lead experimentalist to find new applications of these technologically important materials.

Opracowanie funkcjonałów kosztów równoległego dwuskładnikowego systemu z uwzględnieniem profilaktyki

84%

Kopp W. , Obżerin J. , Pieszczanski A. , Glecz S.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

2002

tom z. 59 [196]

23-28